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प्रश्न
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
उत्तर
`(1 - sin^2 A/cos^2 A)/(cos^2 A/sin^2 A -1) = ((cos^2 A - sin^2 A)/cos^2 A)/((cos^2 A - sin^2 A)/sin^2 A`
`= (sin^2 A)/cos^2 A`
`= tan^2 A`
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Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
